Pith. sign in

REVIEW 8 cited by

Stability of Higher-Dimensional Schwarzschild Black Holes

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv hep-th/0305185 v3 pith:SLXXAKQE submitted 2003-05-20 hep-th gr-qc

Akihiro Ishibashi (Univ. of Cambridge) , Hideo Kodama (Kyoto Univ.) This is my paper · ORCID
classification hep-thgr-qc
keywords blackholesperturbationshigher-dimensionalsymmetricmaximallyperturbationschwarzschild
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We investigate the classical stability of the higher-dimensional Schwarzschild black holes against linear perturbations, in the framework of a gauge-invariant formalism for gravitational perturbations of maximally symmetric black holes, recently developed by the authors. The perturbations are classified into the tensor, vector, and scalar-type modes according to their tensorial behaviour on the spherical section of the background metric, where the last two modes correspond respectively to the axial- and the polar-mode in the four-dimensional situation. We show that, for each mode of the perturbations, the spatial derivative part of the master equation is a positive, self-adjoint operator in the $L^2$-Hilbert space, hence that the master equation for each tensorial type of perturbations does not admit normalisable negative-modes which would describe unstable solutions. On the same Schwarzschild background, we also analyse the static perturbation of the scalar mode, and show that there exists no static perturbation which is regular everywhere outside the event horizon and well-behaved at spatial infinity. This checks the uniqueness of the higher-dimensional spherically symmetric, static, vacuum black hole, within the perturbation framework. Our strategy for the stability problem is also applicable to the other higher-dimensional maximally symmetric black holes with non-vanishing cosmological constant. We show that all possible types of maximally symmetric black holes (thus, including the higher-dimensional Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter black holes) are stable against the tensor and the vector perturbations.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reverse Isoperimetric Conjecture as a Noether-Charge Stability Theorem

    gr-qc 2026-06 unverdicted novelty 7.0 of 10

    The reverse isoperimetric conjecture is proven to be the fixed-volume form of a boundary-completed Noether-charge stability theorem.

  2. Quasinormal modes of Proca and Maxwell fields in $d$-dimensional Schwarzschild-AdS black holes

    gr-qc 2026-05 conditional novelty 7.0 of 10

    Scalar-type Maxwell perturbations in large d≥5 Schwarzschild-AdS black holes exhibit purely imaginary low-frequency quasinormal modes, confirmed numerically and by asymptotic matching.

  3. Dynamical Tidal Response of Schwarzschild Black Holes

    gr-qc 2025-11 conditional novelty 7.0 of 10

    The dynamical Love numbers of a Schwarzschild black hole are nonzero at quadratic order in frequency, run logarithmically with a coefficient set by dissipation, and are now matched including their finite, scheme-depen...

  4. Radial Perturbations of Black Holes in DHOST Theories

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    Radial perturbations of black holes with primary hair in DHOST theories are rewritten as a flat radial wave equation whose positive self-adjoint extension guarantees stability of the monopole mode.

  5. Quasinormal modes and continuum response of de Sitter black holes via complex scaling method

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    Complex scaling unifies quasinormal modes and continuum response for black-hole perturbations in four-dimensional Schwarzschild-de Sitter spacetimes.

  6. Non-oscillatory gravitational quasinormal modes of Reissner-Nordstr\"om-de Sitter spacetime

    gr-qc 2025-06 conditional novelty 6.0 of 10

    Purely imaginary gravitational quasinormal modes of Reissner-Nordström-de Sitter black holes are computed and shown to obey a universal small-hole formula and to generate late-time exponential tails.

  7. Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity

    gr-qc 2026-07 accept novelty 5.0 of 10

    For NED with Maxwell weak-field limit, monopole stability of STT solutions with F=0 is identical to Maxwell-STT, and the zero-charge limit of V_eff erases all NED traces.

  8. Superradiance -- the 2020 Edition

    gr-qc 2015-01 unverdicted novelty 4.0 of 10

    Black-hole superradiance extracts energy via the ergoregion and can trigger instabilities with applications to dark matter, beyond-Standard-Model physics, and laboratory analogs.

Pith tools